Hello all! I'm new and i have me registered because i want to know, if it is possible, with Arduino for STM32 programming for the STM32 F303 processor? This processor is on a flight controller board with the name 'BeeCore' which is on Banggood available. It has a micro usb port. Please answer me.

As far as I can tell the BeeCore uses a STM32F3 which we don't support (at the moment)

You could try koduino, https://github.com/avikde/koduino as their main target processor is the F3.
However there is a lot of variation in the F3 processor range, and the F3 on the BeeCore may not work with Koduino.
(You'd need to ask Avik via github)